This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24-27, 2009, at Yale University. Lie groups and their representations play a fundamental role of mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work. In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.
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978-0-8218-5246-0 (9780821852460)
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Expository papers: The Plancherel formula, the Plancherel theorem, and the Fourier transform of orbital integrals by R. A. Herb and P. J. Sally, Jr. Branching problems of Zuckerman derived functor modules by T. Kobayashi Chiral equivariant cohomology of spheres by B. H. Lian, A. R. Linshaw, and B. Song Research papers: Computing global characters by J. Adams Stable combinations of special unipotent representations by D. M. Barbasch and P. E. Trapa Levi components of parabolic subalgebras of finitary Lie algebras by E. Dan-Cohen and I. Penkov On extending the Langlands-Shahidi method to arithmetic quotients of loop groups by H. Garland The measurement of quantum entanglement and enumeration of graph coverings by M. W. Hero, J. F. Willenbring, and L. K. Williams The dual pair $(O_{p,q}, O\widetilde{Sp}_{2,2})$ and Zuckerman translation by D. Lu and R. Howe On the algebraic set of singular elements in a complex simple Lie algebra by B. Kostant and N. Wallach An explicit embedding of gravity and the standard model in $E_8$ by A. G. Lisi From groups to symmetric spaces by G. Lusztig Study of antiorbital complexes by G. Lusztig Adelization of automorphic distributions and mirabolic Eisenstein series by S. D. Miller and W. Schmid Categories of integrable $sl(\infty)-, o(\infty)-, sp(\infty)$-modules by I. Penkov and V. Serganova Binomial coefficients and Littlewood-Richardson coefficients for interpolation polynomials and Macdonald polynomials by S. Sahi Restriction of some representations of $U(p,q)$ to a symmetric subgroup by B. Speh
